Computing the Characteristic Polynomial of a Finite Rank Two Drinfeld Module

Motivated by finding analogues of elliptic curve point counting techniques, we introduce one deterministic and two new Monte Carlo randomized algorithms to compute the characteristic polynomial of a finite rank-two Drinfeld module. We compare their asymptotic complexity to that of previous algorithms given by Gekeler, Narayanan and Garai-Papikian and discuss their practical behavior. In particular, we find that all three approaches represent either an improvement in complexity or an expansion of the parameter space over which the algorithm may be applied. Some experimental results are also presented

A solvable model for the diffusion and reaction of neurotransmitters in a synaptic junction

<p>Abstract</p> <p>Background</p> <p>The diffusion and reaction of the transmitter acetylcholine in neuromuscular junctions and the diffusion and binding of Ca²⁺in the dyadic clefts of ventricular myocytes have been extensively modeled by Monte Carlo simulations and by finite-difference and finite-element solutions. However, an analytical solution that can serve as a benchmark for testing these numerical methods has been lacking.</p> <p>Result</p> <p>Here we present an analytical solution to a model for the diffusion and reaction of acetylcholine in a neuromuscular junction and for the diffusion and binding of Ca²⁺in a dyadic cleft. Our model is similar to those previously solved numerically and our results are also qualitatively similar.</p> <p>Conclusion</p> <p>The analytical solution provides a unique benchmark for testing numerical methods and potentially provides a new avenue for modeling biochemical transport.</p

Evaluating the Effect of Crutch-using on Trunk Muscle Loads

As a traditional tool of external assistance, crutches play an important role in society. They have a wide range of applications to help either the elderly and disabled to walk or to treat certain illnesses or for post-operative rehabilitation. But there are many different types of crutches, including shoulder crutches and elbow crutches. How to choose has become an issue that deserves to be debated. Because while crutches help people walk, they also have an impact on the body. Inappropriate choice of crutches or long-term misuse can lead to problems such as scoliosis. Previous studies were mainly experimental measurements or the construction of dynamic models to calculate the load on joints with crutches. These studies focus only on the level of the joints, ignoring the role that muscles play in this process. Although some also take into account the degree of muscle activation, there is still a lack of quantitative analysis. The traditional dynamic model can be used to calculate the load on each joint. However, due to the activation of the muscle, this situation only causes part of the load transmitted to the joint, and the work of the chair will compensate the other part of the load. Analysis at the muscle level allows a better understanding of the impact of crutches on the body. By comparing the levels of activation of the trunk muscles, it was found that the use of crutches for walking, especially a single crutch, can cause a large difference in the activation of the back muscles on the left and right sides, and this difference will cause muscle degeneration for a long time, leading to scoliosis. In this article taking scoliosis as an example, by analyzing the muscles around the spine, we can better understand the pathology and can better prevent diseases. The objective of this article is to analyze normal walking compared to walking with one or two crutches using OpenSim software to obtain the degree of activation of different muscles in order to analyze the impact of crutches on the body

The Study of TeV Variability and Duty Cycle of Mrk 421 from 3 Years of Observations with the Milagro Observatory

TeV flaring activity with time scales as short as tens of minutes and an orphan TeV flare have been observed from the blazar Markarian 421 (Mrk 421). The TeV emission from Mrk 421 is believed to be produced by leptonic synchrotron self-Compton (SSC) emission. In this scenario, correlations between the X-ray and the TeV fluxes are expected, TeV orphan flares are hardly explained and the activity (measured as duty cycle) of the source at TeV energies is expected to be equal or less than that observed in X-rays if only SSC is considered. To estimate the TeV duty cycle of Mrk 421 and to establish limits on its variability at different time scales, we continuously observed Mrk 421 with the Milagro observatory. Mrk 421 was detected by Milagro with a statistical significance of 7.1 standard deviations between 2005 September 21 and 2008 March 15. The observed spectrum is consistent with previous observations by VERITAS. We estimate the duty cycle of Mrk 421 for energies above 1 TeV for different hypothesis of the baseline flux and for different flare selections and we compare our results with the X-ray duty cycle estimated by Resconi et al. 2009. The robustness of the results is discussed.Comment: 27 pages, 6 figures, ApJ accepte

Spectrum and Morphology of the Two Brightest Milagro Sources in the Cygnus Region: MGRO J2019+37 and MGRO J2031+41

The Cygnus region is a very bright and complex portion of the TeV sky, host to unidentified sources and a diffuse excess with respect to conventional cosmic-ray propagation models. Two of the brightest TeV sources, MGRO J2019+37 and MGRO J2031+41, are analyzed using Milagro data with a new technique, and their emission is tested under two different spectral assumptions: a power law and a power law with an exponential cutoff. The new analysis technique is based on an energy estimator that uses the fraction of photomultiplier tubes in the observatory that detect the extensive air shower. The photon spectrum is measured in the range 1 to 200 TeV using the last 3 years of Milagro data (2005-2008), with the detector in its final configuration. MGRO J2019+37 is detected with a significance of 12.3 standard deviations ($\sigma$), and is better fit by a power law with an exponential cutoff than by a simple power law, with a probability $>98$% (F-test). The best-fitting parameters for the power law with exponential cutoff model are a normalization at 10 TeV of $7^{+5}_{-2}\times10^{-10}$ $\mathrm{s^{-1}\: m^{-2}\: TeV^{-1}}$, a spectral index of $2.0^{+0.5}_{-1.0}$ and a cutoff energy of $29^{+50}_{-16}$ TeV. MGRO J2031+41 is detected with a significance of 7.3$\sigma$, with no evidence of a cutoff. The best-fitting parameters for a power law are a normalization of $2.4^{+0.6}_{-0.5}\times10^{-10}$ $\mathrm{s^{-1}\: m^{-2}\: TeV^{-1}}$ and a spectral index of $3.08^{+0.19}_{-0.17}$. The overall flux is subject to an $\sim$30% systematic uncertainty. The systematic uncertainty on the power law indices is $\sim$0.1. A comparison with previous results from TeV J2032+4130, MGRO J2031+41 and MGRO J2019+37 is also presented.Comment: 11 pages, 10 figure

Calibration of the Milagro Cosmic Ray Telescope

The Milagro detector is an air shower array which uses the water Cherenkov technique and is capable of continuously monitoring the sky at energies near 1 TeV. The detector consists of 20000 metric tons of pure water instrumented with 723 photo-multiplier tubes (PMTs). The PMTs are arranged in a two-layer structure on a lattice of 3 m spacing covering 5000 $m^2$ area. The direction of the shower is determined from the relative timing of the PMT signals, necessitating a common time reference and amplitude slewing corrections to improve the time resolution. The calibration system to provide these consists of a pulsed laser driving 30 diffusing light sources deployed in the pond to allow cross-calibration of the PMTs. The system is capable of calibrating times and the pulse-heights from the PMTs using the time-over-threshold technique. The absolute energy scale is provided using single muons passing through the detector. The description of the calibration system of the Milagro detector and its prototype Milagrito will be presented.Comment: 4 pages, submitted to the XXVI International Cosmic Ray Conferenc

Study of the Shadows of the Moon and the Sun with VHE Cosmic Rays

Milagrito, a prototype for the Milagro detector, operated for 15 months in 1997-8 and collected 8.9 billion events. It was the first extensive air shower (EAS) array sensitive to showers intiated by primaries with energy below 1 TeV. The shadows of the sun and moon observed with cosmic rays can be used to study systematic pointing shifts and measure the angular resolution of EAS arrays. Below a few TeV, the paths of cosmic rays coming toward the earth are bent by the helio- and geo-magnetic fields. This is expected to distort and displace the shadows of the sun and the moon. The moon shadow, offset from the nominal (undeflected) position, has been observed with high statistical significance in Milagrito. This can be used to establish energy calibrations, as well as to search for the anti-matter content of the VHE cosmic ray flux. The shadow of the sun has also been observed with high significance.Comment: 4 pages, submitted to XXVI International Cosmic Ray Conference, Salt Lake Cit

Evidence for TeV Emission from GRB 970417a

Milagrito, a detector sensitive to very high energy gamma rays, monitored the northern sky from February 1997 through May 1998. With a large field of view and a high duty cycle, this instrument was well suited to perform a search for TeV gamma-ray bursts (GRBs). We report on a search made for TeV counterparts to GRBs observed by BATSE. BATSE detected 54 GRBs within the field of view of Milagrito during this period. An excess of events coincident in time and space with one of these bursts, GRB 970417a, was observed by Milagrito. The excess has a chance probability of $2.8 \times 10^{-5}$ of being a fluctuation of the background. The probability for observing an excess at least this large from any of the 54 bursts is $1.5 \times 10^{-3}$. No significant correlations were detected from the other bursts.Comment: 10 pages, 3 figure